Predicting the Price of Semiconductor Stocks
Chris Dare
2024-05-10
Introduction
With the growing presence of technology in our society, there is an rapidly increasing demand for hardware which supports our heavy computational demands. One of the most important pieces of computer hardware for computationally-intensive tasks is Graphics Processing Units (GPU) due to their ability to handle a wide range of parallel processing tasks — this has made them an invaluable resource for companies pursing any sort of Artificial Intelligence (AI), super-computing, crypto-currencies, or computer graphics. Consequently, companies which manufacture processing chips have been a focal point for investors in recent years, as they directly control the output capabilities for a large portion of the technology sector.
The purpose of this project is to attempt to predict the price-trends of a semiconductor stock - in fact, there are actually four stocks we wish to predict: Nvidia, Advanced Micro Devices (AMD), Intel Corporation, and Taiwan Semiconductor Manufacturing. Though tackling four separate stocks slightly deviates from the project guideline of applying a variety of machine learning algorithms to a single data-set, the hope is that this will give a better prediction of which machine learning models are most useful for stock market prediction (in the case of semiconductor stocks). Put differently, if we only applied our statistical learning models to a single stock resulting in an optimal model \(M\), this would naturally raise the question of whether \(M\) fits the stock best because it is optimal for stock market predictions, or if it fits the stock best due to the stock’s characteristics. Therefore, for each of the four chip manufacturers listed above, we will apply a variety of statistical learning models , ranging from standard regression to more non-linear models like random forest learning and k-Nearest neighbors.
Loading Packages and Data
knitr::opts_chunk$set(echo = TRUE)
library(tidyverse)
library(tidymodels)
library(ggplot2)
library(corrplot)
library(discrim)
library(ggthemes)
library(kableExtra)
library(yardstick)
library(visdat)
library(scales)
library(glmnet)
library(quantmod)
library(dygraphs)
library(tidyr)
tidymodels_prefer()
conflicted::conflicts_prefer(yardstick::rsq)
conflicted::conflicts_prefer(dplyr::lag)
set.seed(3435)One of the most useful packages for the analysis of stock market data
in R is the quantmod package. While there are several
built-in functions and tools which predict stock market trends using
statistical learning, we will simply use this package for the purpose of
pulling live stock data from Yahoo
Finance and visualizing the data in a much neater fashion than usual
ggplot2 (as using built-in statistical learning methods in
a statistical learning project is somewhat poor form).
In particular, the quantmod package allows us to
circumvent the process of downloading a CSV file of stock market data
from the internet and read it into R by instead using the
loadSymbols method, which then automatically loads all
stock data (over a potentially specified interval) into a table assigned
the same name as the stock’s symbol. Since the function
loadSymbols will automatically set the most recent day to
pull stock data as the current day, we must specify a “last day” to pull
our stock data to ensure that our models run the same every day; thus,
we will pull one fiscal year’s worth of stock data
ranging from January \(1^{\text{st}}\),
2023 to January \(1^{\text{st}}\),
2024. It is worth noting that the table loaded by
loadSymbols is not a data-frame; its
original datatype must be used for other functions in the
quantmod package such as the chartSeries plots
applied below, but we will later need to typecast this object to a usual
data-frame in order to apply most of the tidyverse
functions.
Below are formatted plots of the market data for our four stocks
(AMD, NVDA, INTC, and TSM) obtained using the chartSeries
function. We will postpone the discussion of what several terms mean
until the Exploratory Data Analysis section.
a<-loadSymbols("AMD", from="2023-01-01", to="2024-01-01")
chartSeries(AMD,TA=c(addVo(),addBBands(),addMACD()))
my_dates <- index(AMD)
AMD <- data.frame(AMD)
AMD$AMD.Date <- my_datesa<-loadSymbols("NVDA", from="2023-01-01", to="2024-01-01")
chartSeries(NVDA,TA=c(addVo(),addBBands(),addMACD()))
NVDA <- data.frame(NVDA)
NVDA$NVDA.Date <- my_datesa<-loadSymbols("INTC", from="2023-01-01", to="2024-01-01")
chartSeries(INTC,TA=c(addVo(),addBBands(),addMACD()))
INTC <- data.frame(INTC)
INTC$INTC.Date <- my_datesa<-loadSymbols("TSM", from="2023-01-01", to="2024-01-01")
chartSeries(TSM,TA=c(addVo(),addBBands(),addMACD()))
TSM <- data.frame(TSM)
TSM$TSM.Date <- my_datesWith each stock’s data loaded and typecast into a data-frame, we also
want to examine the total number of predictors and observations for each
individual stock. As the beginning and ending dates specified in
loadSymbols are the same across our four stocks, it
suffices to check the dimensions of only one of our data frames:
dim(AMD)## [1] 250 7One may be initially misled by the fact that only 250 observations appear across a years worth of data; i.e. we only have 250 out of 365 days. However, this is simply a reflection of the fact that the New York Stock Exchange does not operate on weekends and a hanful of holidays. In addition, a quick analysis shows that there is no missing data among any of the four stocks; this is somewhat expected since stock market data is meant to be as publicly available as possible and the original features are fairly common metrics for financial institutions to collect.
vis_miss(AMD)
vis_miss(NVDA)
vis_miss(INTC)
vis_miss(TSM)
Exploratory Data Analysis
With our four stocks pulled and loaded into data frames, we first wish to examine the relevance of each predictor initially provided and then examine other possible metrics to measure the performance of a given stock by. As measuring the performance of a financial security over time relies on not only historical data, but historical data whose relevancy may depreciate depending on how recent it is (or isn’t), much of the rationale behind our added predictors in the latter half of this section revolves around study of time-series in statistics. However, since the focus of this project is on statistical-learning models and how they are applied to certain problems, several important techniques in the study of time-series (and thus stock-market analysis) will not be applied within this project.
Describing the Predictors
In the first half of this section, we first examine the initial
predictors loaded into the the data frames for our stocks. For each of
the four stock symbols (AMD, NVDA, INTC, and TSM), we only consider the
term following the delimiter "." and our stock symbol:
Open: The opening price of the stock that day (specifically, the value of the stock at 9:30AM EST).Close: The closing price of the stock that day (specifically, the value of the stock at 4:00PM EST)Low: The minimum valuation of the stock over the given day.High: The maximum valuation of the stock over the given day.Volume: The total number of shares traded on a stock over the given day (i.e. both bought and sold).Adjusted: The closing price of the stock that day together with any adjustments due to corporate actions such as rights offerings, dividends, and splits.
The dygraph package loaded in the previous section
provides a compact and convenient way for us to measure several of the
above predictors simultaneously for each stock:
p <- dygraph(AMD[,c(1:4)], xlab = "Date", ylab = "Price", main = "AMD Price") %>%
dySeries("AMD.Open", label = "Open", color = "black") %>%
dySeries("AMD.Low", label = "Low", color = "red") %>%
dySeries("AMD.High", label = "High", color = "green") %>%
dySeries("AMD.Close", label = "Close", color = "orange") %>%
dyRangeSelector() %>%
dyCandlestick()%>%
dyCrosshair(direction = "vertical") %>%
dyHighlight(highlightCircleSize = 3, highlightSeriesBackgroundAlpha = 0.2, hideOnMouseOut = T) %>%
dyRoller(rollPeriod = 1)
pp <- dygraph(NVDA[,c(1:4)], xlab = "Date", ylab = "Price", main = "NVDA Price") %>%
dySeries("NVDA.Open", label = "Open", color = "black") %>%
dySeries("NVDA.Low", label = "Low", color = "red") %>%
dySeries("NVDA.High", label = "High", color = "green") %>%
dySeries("NVDA.Close", label = "Close", color = "orange") %>%
dyRangeSelector() %>%
dyCandlestick()%>%
dyCrosshair(direction = "vertical") %>%
dyHighlight(highlightCircleSize = 3, highlightSeriesBackgroundAlpha = 0.2, hideOnMouseOut = T) %>%
dyRoller(rollPeriod = 1)
pp <- dygraph(INTC[,c(1:4)], xlab = "Date", ylab = "Price", main = "INTC Price") %>%
dySeries("INTC.Open", label = "Open", color = "black") %>%
dySeries("INTC.Low", label = "Low", color = "red") %>%
dySeries("INTC.High", label = "High", color = "green") %>%
dySeries("INTC.Close", label = "Close", color = "orange") %>%
dyRangeSelector() %>%
dyCandlestick()%>%
dyCrosshair(direction = "vertical") %>%
dyHighlight(highlightCircleSize = 3, highlightSeriesBackgroundAlpha = 0.2, hideOnMouseOut = T) %>%
dyRoller(rollPeriod = 1)
pp <- dygraph(TSM[,c(1:4)], xlab = "Date", ylab = "Price", main = "TSM Price") %>%
dySeries("TSM.Open", label = "Open", color = "black") %>%
dySeries("TSM.Low", label = "Low", color = "red") %>%
dySeries("TSM.High", label = "High", color = "green") %>%
dySeries("TSM.Close", label = "Close", color = "orange") %>%
dyRangeSelector() %>%
dyCandlestick()%>%
dyCrosshair(direction = "vertical") %>%
dyHighlight(highlightCircleSize = 3, highlightSeriesBackgroundAlpha = 0.2, hideOnMouseOut = T) %>%
dyRoller(rollPeriod = 1)
pAdded Predictors and Metrics
While the six predictors pulled from Yahoo Finance give significant insight into each stock’s historical performance over the year, there may be other, more useful metrics that we can use to assess the future growth of our securities. For example, we are attempting to predict data which relies on it’s past/recent behavior; however, all of the variables in our data frame are synchronized to measure the same 24-hour window. This issue naturally leads to the study of time series in statistics, which will ultimately motivate several of the variables we introduce. There are, however, other metrics we will introduce that are much more specific to the study of stock market data and not time series as a whole.
Lag Values
As mentioned above, the analysis of stock market data is a problem which falls into the branch of statistics known as time-series. Ultimately, the study of time-series is a vast and rich topic that we cannot hope to even begin covering within the scope of this project; however, we will attempt to provide a rudimentary explanation of the necessary topics for the sake of completeness.
Foremost, a time series is a collection of data points \(\{ X_t : t \in T \}\) gathered over some time domain \(T \subseteq [0, \infty)\) and ordered chronologically; while it is not necessarily intrinsic of general time series, many examples have the property that the value of a given data point \(X_{t_0}\) depends on previous historical data \(\{ X_t : t < t_0 \}\). For these types of examples, whenever we are given sample of data points \(\{ X_1, X_2, \dots, X_n \}\) ordered chronologically we refer to \(X_{i-1}, X_{i-2}, \dots, X_{i-p}\) as the lag variables associated to \(X_i\). Conveniently, this allows us to model \(X_i\) as a function of its lag variables; for example, autoregression is simply the study of regression techniques applied to the lag variables (and potentially other predictors) of a time-series.
As many of the computations in R are done via vector operations
(i.e. on the columns of a data frame), defining a lag variable is
effectively synonymous to shifting the values in a given vector “down”.
While this would likely require some sort of for-loop
operation in other languages, R provides the useful lag
method to do exactly this. However, there is one shortcoming that arises
regardless of the language used: how do we define the lag variable for
the first observation? In R, since we are shifting a given vector down
by \(p\) entries, the first \(p-1\) entries of the lag variable are
filled in with NA which can ultimately cause some issues
for numerical computations later down the road. One common fix for this
is to simply pretend the model was constant prior to the first
observation, and define the lag variables \(X_{1 - p} = X_1\) — this can be done in R
using the fill command. It should be noted that assuming
the model is constant prior to the first observation is a fairly
rudimentary solution, and there are more advanced techniques which may
give better accuracy.
# Define lag variables for AMD
AMD$AMD.Close_L1 <- lag(AMD$AMD.Close, 1)
AMD$AMD.Close_L2 <- lag(AMD$AMD.Close, 2)
AMD$AMD.Close_L3 <- lag(AMD$AMD.Close, 3)
AMD$AMD.Close_L4 <- lag(AMD$AMD.Close, 4)
AMD$AMD.Close_L5 <- lag(AMD$AMD.Close, 5)
AMD$AMD.Close_L6 <- lag(AMD$AMD.Close, 6)
AMD$AMD.Close_L7 <- lag(AMD$AMD.Close, 7)
AMD$AMD.Close_L8 <- lag(AMD$AMD.Close, 8)
AMD$AMD.Close_L9 <- lag(AMD$AMD.Close, 9)
AMD$AMD.Close_L10 <- lag(AMD$AMD.Close, 10)
# Fill in NA entries in beginning of lag variables
AMD <- AMD %>%
fill(AMD.Close_L1, .direction = "up") %>%
fill(AMD.Close_L2, .direction = "up") %>%
fill(AMD.Close_L3, .direction = "up") %>%
fill(AMD.Close_L4, .direction = "up") %>%
fill(AMD.Close_L5, .direction = "up") %>%
fill(AMD.Close_L6, .direction = "up") %>%
fill(AMD.Close_L7, .direction = "up") %>%
fill(AMD.Close_L8, .direction = "up") %>%
fill(AMD.Close_L9, .direction = "up") %>%
fill(AMD.Close_L10, .direction = "up")
# Define lag variables for NVDA
NVDA$NVDA.Close_L1 <- lag(NVDA$NVDA.Close, 1)
NVDA$NVDA.Close_L2 <- lag(NVDA$NVDA.Close, 2)
NVDA$NVDA.Close_L3 <- lag(NVDA$NVDA.Close, 3)
NVDA$NVDA.Close_L4 <- lag(NVDA$NVDA.Close, 4)
NVDA$NVDA.Close_L5 <- lag(NVDA$NVDA.Close, 5)
NVDA$NVDA.Close_L6 <- lag(NVDA$NVDA.Close, 6)
NVDA$NVDA.Close_L7 <- lag(NVDA$NVDA.Close, 7)
NVDA$NVDA.Close_L8 <- lag(NVDA$NVDA.Close, 8)
NVDA$NVDA.Close_L9 <- lag(NVDA$NVDA.Close, 9)
NVDA$NVDA.Close_L10 <- lag(NVDA$NVDA.Close, 10)
# Fill in NA entries
NVDA <- NVDA %>%
fill(NVDA.Close_L1, .direction = "up") %>%
fill(NVDA.Close_L2, .direction = "up") %>%
fill(NVDA.Close_L3, .direction = "up") %>%
fill(NVDA.Close_L4, .direction = "up") %>%
fill(NVDA.Close_L5, .direction = "up") %>%
fill(NVDA.Close_L6, .direction = "up") %>%
fill(NVDA.Close_L7, .direction = "up") %>%
fill(NVDA.Close_L8, .direction = "up") %>%
fill(NVDA.Close_L9, .direction = "up") %>%
fill(NVDA.Close_L10, .direction = "up")
# Define lag variables for INTC
INTC$INTC.Close_L1 <- lag(INTC$INTC.Close, 1)
INTC$INTC.Close_L2 <- lag(INTC$INTC.Close, 2)
INTC$INTC.Close_L3 <- lag(INTC$INTC.Close, 3)
INTC$INTC.Close_L4 <- lag(INTC$INTC.Close, 4)
INTC$INTC.Close_L5 <- lag(INTC$INTC.Close, 5)
INTC$INTC.Close_L6 <- lag(INTC$INTC.Close, 6)
INTC$INTC.Close_L7 <- lag(INTC$INTC.Close, 7)
INTC$INTC.Close_L8 <- lag(INTC$INTC.Close, 8)
INTC$INTC.Close_L9 <- lag(INTC$INTC.Close, 9)
INTC$INTC.Close_L10 <- lag(INTC$INTC.Close, 10)
# Fill in NA entries
INTC <- INTC %>%
fill(INTC.Close_L1, .direction = "up") %>%
fill(INTC.Close_L2, .direction = "up") %>%
fill(INTC.Close_L3, .direction = "up") %>%
fill(INTC.Close_L4, .direction = "up") %>%
fill(INTC.Close_L5, .direction = "up") %>%
fill(INTC.Close_L6, .direction = "up") %>%
fill(INTC.Close_L7, .direction = "up") %>%
fill(INTC.Close_L8, .direction = "up") %>%
fill(INTC.Close_L9, .direction = "up") %>%
fill(INTC.Close_L10, .direction = "up")
# Define lag variables for TSM
TSM$TSM.Close_L1 <- lag(TSM$TSM.Close, 1)
TSM$TSM.Close_L2 <- lag(TSM$TSM.Close, 2)
TSM$TSM.Close_L3 <- lag(TSM$TSM.Close, 3)
TSM$TSM.Close_L4 <- lag(TSM$TSM.Close, 4)
TSM$TSM.Close_L5 <- lag(TSM$TSM.Close, 5)
TSM$TSM.Close_L6 <- lag(TSM$TSM.Close, 6)
TSM$TSM.Close_L7 <- lag(TSM$TSM.Close, 7)
TSM$TSM.Close_L8 <- lag(TSM$TSM.Close, 8)
TSM$TSM.Close_L9 <- lag(TSM$TSM.Close, 9)
TSM$TSM.Close_L10 <- lag(TSM$TSM.Close, 10)
# Fill in NA entries
TSM <- TSM %>%
fill(TSM.Close_L1, .direction = "up") %>%
fill(TSM.Close_L2, .direction = "up") %>%
fill(TSM.Close_L3, .direction = "up") %>%
fill(TSM.Close_L4, .direction = "up") %>%
fill(TSM.Close_L5, .direction = "up") %>%
fill(TSM.Close_L6, .direction = "up") %>%
fill(TSM.Close_L7, .direction = "up") %>%
fill(TSM.Close_L8, .direction = "up") %>%
fill(TSM.Close_L9, .direction = "up") %>%
fill(TSM.Close_L10, .direction = "up") Any time one is utilizing lag variables in a time series problem, a natural question which arises is “how far back should we look to measure current data”? In other words, what is the optimal lag length \(p\) for a given time series. It turns out this an incredibly involved problem that does not have a single universal answer for all time-series based questions; there are several advanced techniques guided by economic theory for auto-regressive models such as the F-test approach and Bayes information criterion (BIC) / Akaike information criterion (AIC) that are often used, but we will unfortunately omit any discussion of these techniques since the focus of this project is on the statistical learning models themselves. Instead, we will naively take the lag length to be two weeks (i.e. 10 business days) which is fairly short for economic time series problems measured on a daily scale.
Simple Moving Average of Closing Price
One issue that immediately arises after defining lag variables is that they are almost always highly correlated with one another. Ultimately this makes sense, as they are in fact measuring the same continuous observable; however, adding lag variables often results in a significant amount of multicollinearity within our model. One way to eliminate this issue is to instead measure the average of our lag variables across a potentially different lag length, known as the simple moving average (SMA). Specifically, we define \[ \operatorname{SMA}(X_i, k) = \frac{1}{k}\sum_{j=0}^{k-1}X_{i-j} \] (notice this is inclusive of the current data point, but we could alternatively define the simple moving average to run over \(1 \leq j \leq k\) to specifically account for prior data).
simple_moving_average <- function(my_vec, lag_period) {
#' Takes the running average of a column vector
#'
#' Creates a new column vector whose entries are the average of the previous lag_period entries.
#' When not enough data is available to take the average over lag_period, the closest possible
#' average will be taken (for example, if lag_period = 10, then the first 2nd entry of the output
#' vector will simply be the average of the first two values, the 3rd entry of the output vector
#' will be the average of the first three values, and so forth.)
#'
#' @param my_vec the column vector to take the average values of
#' @param lag_period the number of days one wishes to average over
#'
#' @return A vector whose entries represent the average of the previous lag_period entries in my_vec
# Error handling
if(is.vector(my_vec) == FALSE){
stop("Not Vector: First argument of simple_moving_average must be a vector")
}
if(is.numeric(my_vec[1]) == FALSE){
stop("Non-numeric Entries: values of vector in first argument must be numeric.")
}
if(is.numeric(lag_period) == FALSE || lag_period != round(lag_period)){
stop("Not Integer: Second argument of simple_moving_average must be an integer larger than or equal to 2")
}
if(lag_period <= 1){
stop("Not Large Enough: Second argument of simple_moving_average must be an integer larger than or equal to 2")
}
# return variable
output_vec = c()
for (i in 1:length(my_vec)) {
# If there are less that lag_period of data previous to the current date,
# simply take the average of all the days prior to get the closest thing
# to a running average
if (i <= lag_period){
output_vec[i] = mean(my_vec[1:i])
}
else {
output_vec[i] = mean(my_vec[(i-lag_period + 1):i])
}
}
return(output_vec)
}
# Obtain four simple moving averages of AMD
AMD$AMD.SMA_cl_1W <- simple_moving_average(AMD$AMD.Close, 5)
AMD$AMD.SMA_cl_2W <- simple_moving_average(AMD$AMD.Close, 10)
AMD$AMD.SMA_cl_1M <- simple_moving_average(AMD$AMD.Close, 20)
AMD$AMD.SMA_cl_2M <- simple_moving_average(AMD$AMD.Close, 40)
# Obtain four simple moving averages of NVDA
NVDA$NVDA.SMA_cl_1W <- simple_moving_average(NVDA$NVDA.Close, 5)
NVDA$NVDA.SMA_cl_2W <- simple_moving_average(NVDA$NVDA.Close, 10)
NVDA$NVDA.SMA_cl_1M <- simple_moving_average(NVDA$NVDA.Close, 20)
NVDA$NVDA.SMA_cl_2M <- simple_moving_average(NVDA$NVDA.Close, 40)
# Obtain four simple moving averages of INTC
INTC$INTC.SMA_cl_1W <- simple_moving_average(INTC$INTC.Close, 5)
INTC$INTC.SMA_cl_2W <- simple_moving_average(INTC$INTC.Close, 10)
INTC$INTC.SMA_cl_1M <- simple_moving_average(INTC$INTC.Close, 20)
INTC$INTC.SMA_cl_2M <- simple_moving_average(INTC$INTC.Close, 40)
# Obtain four simple moving averages of TSM
TSM$TSM.SMA_cl_1W <- simple_moving_average(TSM$TSM.Close, 5)
TSM$TSM.SMA_cl_2W <- simple_moving_average(TSM$TSM.Close, 10)
TSM$TSM.SMA_cl_1M <- simple_moving_average(TSM$TSM.Close, 20)
TSM$TSM.SMA_cl_2M <- simple_moving_average(TSM$TSM.Close, 40)
# Plot the simple moving averages for each stock
ggplot(data = AMD, aes(x=AMD.Date)) +
geom_line(aes(y = AMD.SMA_cl_1W, color = '1-Week')) +
geom_line(aes(y = AMD.SMA_cl_2W, color = '2-Week')) +
geom_line(aes(y = AMD.SMA_cl_1M, color = '1-Month')) +
geom_line(aes(y = AMD.SMA_cl_2M, color = '2-Month')) +
ylab('USD') +
scale_color_manual(values = c(
'1-Week' = 'firebrick1',
'2-Week' = 'chocolate1',
'1-Month' = 'gold',
'2-Month' = 'chartreuse'
)) +
xlab('Date') +
ggtitle("(AMD) Simple Moving Average") +
scale_y_continuous( labels = label_comma()) +
theme_dark()
ggplot(data = NVDA, aes(x=NVDA.Date)) +
geom_line(aes(y = NVDA.SMA_cl_1W, color = '1-Week')) +
geom_line(aes(y = NVDA.SMA_cl_2W, color = '2-Week')) +
geom_line(aes(y = NVDA.SMA_cl_1M, color = '1-Month')) +
geom_line(aes(y = NVDA.SMA_cl_2M, color = '2-Month')) +
ylab('USD') +
scale_color_manual(values = c(
'1-Week' = 'firebrick1',
'2-Week' = 'chocolate1',
'1-Month' = 'gold',
'2-Month' = 'chartreuse'
)) +
xlab('Date') +
ggtitle("(NVDA) Simple Moving Average") +
scale_y_continuous( labels = label_comma()) +
theme_dark()
ggplot(data = INTC, aes(x=INTC.Date)) +
geom_line(aes(y = INTC.SMA_cl_1W, color = '1-Week')) +
geom_line(aes(y = INTC.SMA_cl_2W, color = '2-Week')) +
geom_line(aes(y = INTC.SMA_cl_1M, color = '1-Month')) +
geom_line(aes(y = INTC.SMA_cl_2M, color = '2-Month')) +
ylab('USD') +
scale_color_manual(values = c(
'1-Week' = 'firebrick1',
'2-Week' = 'chocolate1',
'1-Month' = 'gold',
'2-Month' = 'chartreuse'
)) +
xlab('Date') +
ggtitle("(INTC) Simple Moving Average") +
scale_y_continuous( labels = label_comma()) +
theme_dark()
ggplot(data = TSM, aes(x=TSM.Date)) +
geom_line(aes(y = TSM.SMA_cl_1W, color = '1-Week')) +
geom_line(aes(y = TSM.SMA_cl_2W, color = '2-Week')) +
geom_line(aes(y = TSM.SMA_cl_1M, color = '1-Month')) +
geom_line(aes(y = TSM.SMA_cl_2M, color = '2-Month')) +
ylab('USD') +
scale_color_manual(values = c(
'1-Week' = 'firebrick1',
'2-Week' = 'chocolate1',
'1-Month' = 'gold',
'2-Month' = 'chartreuse'
)) +
xlab('Date') +
ggtitle("(TSM) Simple Moving Average") +
scale_y_continuous(labels = label_comma()) +
theme_dark()
One characteristic that immediately becomes apparent is that evaluating the simple moving averages instead of the closing costs seems to “smooth out” the curves — in other words, the simple moving average average is much more stable and is not affected by a share’s volatility as much as our original predictors. Mathematically, this is simply a consequence of the fact that we are slowly interpolating the data with the overall average; since the overall average is a constant function (and thus infinitely differentiable), the “smoothing out” process really just us interpolating with a \(C^\infty(\mathbb{R})\) function.
Taking different values for the “lag period” of the simple moving average also has several benefits. Since the simple moving average measures the trends of a stock over that lag period, the simple moving average taken over 2 months (i.e. roughly 40 business days) measures long term behavior much more accurately than the simply moving average taken over 2 weeks (i.e. roughly 10 business days) , which would be a much better measure of short term trends. In fact, two SMA curves crossing tends to be a common trading signal for investors — when a short-period SMA curve crosses below a long-period SMA curve, this indicates the recent behavior of the stock is performing worse than its long term trends, meaning an investor would want to short the stock (i.e. invest based on the assumption the value of the stock will decrease). Similarly, when a short-period SMA curve crosses above a long-period SMA curve, this should indicate to investors that the stock is performing better than usual and thus it is a good idea to go long (i.e. purchase the stock ).
Exponential Moving Average
While the simple moving average (SMA) above can be incredibly useful to de-correlate the lag variables and measure the trends and behaviors of a given security, it can fall short in one particular way: it gives equal weight to events that happened at the beginning of the lag period as it does to events that happened at the end of the lag period. This is generally not the case with time series problems, as the relevancy of data points tends to decay non-linearly over time. A better model would be to weight recent events more heavily than events further in the past, and then take the average of these \(\text{values} \times \text{weights}\) — this is precisely the idea behind the exponential moving average. Specifically, we fix some smoothing factor \(\beta > 0\) define our weight to be \(w = \beta\, /\, (n+1)\) and the exponential moving average as \[ \operatorname{EMA}(X_i, n) = w \cdot X_{i}\ +\ (1-w) \cdot\operatorname{EMA}(X_{i-1}, n) \] where \(n\) is the number of days in our lag period. Its common in finance to take \(\beta = 2\), which is precisely the value we will take for the purpose of this project.
exponential_moving_average_helper <- function(my_vec, lag_period, smoothing_factor) {
#' Helper function to evaluate the exponential moving average over a fixed period
#' using an array buffer
#'
#' Creates a new column vector whose entries are the average of the previous lag_period entries.
#' When not enough data is available to take the average over lag_period, the closest possible
#' average will be taken (for example, if lag_period = 10, then the first 2nd entry of the output
#' vector will simply be the average of the first two values, the 3rd entry of the output vector
#' will be the average of the first three values, and so forth.)
#'
#' @param my_vec the column vector to take the average values of
#' @param lag_period the number of days one wishes to average over
#'
#' @return A vector whose entries represent the average of the previous lag_period entries in my_vec
# Error handling
if(is.vector(my_vec) == FALSE){
stop("Not Vector: First argument of simple_moving_average must be a vector")
}
if(is.numeric(my_vec[1]) == FALSE){
stop("Non-numeric Entries: values of vector in first argument must be numeric.")
}
if(is.numeric(lag_period) == FALSE || lag_period != round(lag_period)){
stop("Not Integer: Second argument of simple_moving_average must be an integer larger than or equal to 2")
}
if(lag_period <= 1){
stop("Not Large Enough: Second argument of simple_moving_average must be an integer larger than or equal to 2")
}
vec_len <- length(my_vec)
output_vec <- c()
output_vec[1] <- my_vec[1]
for (i in 2:vec_len) {
output_vec[i] <- smoothing_factor * my_vec[i] + (1 - smoothing_factor) * output_vec[i-1]
}
return(output_vec[vec_len])
}
exponential_moving_average <- function(my_vec, lag_period) {
#' Takes the running average of a column vector
#'
#' Creates a new column vector whose entries are the average of the previous lag_period entries.
#' When not enough data is available to take the average over lag_period, the closest possible
#' average will be taken (for example, if lag_period = 10, then the first 2nd entry of the output
#' vector will simply be the average of the first two values, the 3rd entry of the output vector
#' will be the average of the first three values, and so forth.)
#'
#' @param my_vec the column vector to take the average values of
#' @param lag_period the number of days one wishes to average over
#'
#' @return A vector whose entries represent the average of the previous lag_period entries in my_vec
# Error handling
if(is.vector(my_vec) == FALSE){
stop("Not Vector: First argument of simple_moving_average must be a vector")
}
if(is.numeric(my_vec[1]) == FALSE){
stop("Non-numeric Entries: values of vector in first argument must be numeric.")
}
if(is.numeric(lag_period) == FALSE || lag_period != round(lag_period)){
stop("Not Integer: Second argument of simple_moving_average must be an integer larger than or equal to 2")
}
if(lag_period <= 1){
stop("Not Large Enough: Second argument of simple_moving_average must be an integer larger than or equal to 2")
}
output_vec <- c()
output_vec[1] <- my_vec[1]
smoothing_factor = 2/(lag_period+1)
for (i in 2:length(my_vec)) {
# If there are less that lag_period of data previous to the current date,
# simply take the average of all the days prior to get the closest thing
# to a running average
if (i <= lag_period){
output_vec[i] = exponential_moving_average_helper(my_vec[1:i], i, 2/(i + 1))
}
else {
output_vec[i] = exponential_moving_average_helper(my_vec[(i-lag_period + 1):i], lag_period, smoothing_factor)
}
}
return(output_vec)
}
# Compute Exponential moving average for AMD
AMD$AMD.EMA_cl_1W <- exponential_moving_average(AMD$AMD.Close, 5)
AMD$AMD.EMA_cl_2W <- exponential_moving_average(AMD$AMD.Close, 10)
AMD$AMD.EMA_cl_1M <- exponential_moving_average(AMD$AMD.Close, 20)
AMD$AMD.EMA_cl_2M <- exponential_moving_average(AMD$AMD.Close, 40)
# Compute Exponential moving average for NVDA
NVDA$NVDA.EMA_cl_1W <- exponential_moving_average(NVDA$NVDA.Close, 5)
NVDA$NVDA.EMA_cl_2W <- exponential_moving_average(NVDA$NVDA.Close, 10)
NVDA$NVDA.EMA_cl_1M <- exponential_moving_average(NVDA$NVDA.Close, 20)
NVDA$NVDA.EMA_cl_2M <- exponential_moving_average(NVDA$NVDA.Close, 40)
# Compute Exponential moving average for INTC
INTC$INTC.EMA_cl_1W <- exponential_moving_average(INTC$INTC.Close, 5)
INTC$INTC.EMA_cl_2W <- exponential_moving_average(INTC$INTC.Close, 10)
INTC$INTC.EMA_cl_1M <- exponential_moving_average(INTC$INTC.Close, 20)
INTC$INTC.EMA_cl_2M <- exponential_moving_average(INTC$INTC.Close, 40)
# Compute Exponential moving average for TSM
TSM$TSM.EMA_cl_1W <- exponential_moving_average(TSM$TSM.Close, 5)
TSM$TSM.EMA_cl_2W <- exponential_moving_average(TSM$TSM.Close, 10)
TSM$TSM.EMA_cl_1M <- exponential_moving_average(TSM$TSM.Close, 20)
TSM$TSM.EMA_cl_2M <- exponential_moving_average(TSM$TSM.Close, 40)
# Plot the exponential moving average for each stock
ggplot(data = AMD, aes(x=AMD.Date)) +
geom_line(aes(y = AMD.EMA_cl_1W, color = '1-Week')) +
geom_line(aes(y = AMD.EMA_cl_2W, color = '2-Week')) +
geom_line(aes(y = AMD.EMA_cl_1M, color = '1-Month')) +
geom_line(aes(y = AMD.EMA_cl_2M, color = '2-Month')) +
ylab('USD') +
scale_color_manual(values = c(
'1-Week' = 'firebrick1',
'2-Week' = 'chocolate1',
'1-Month' = 'gold',
'2-Month' = 'chartreuse'
)) +
xlab('Date') +
ggtitle("(AMD) Exponential Moving Average") +
scale_y_continuous( labels = label_comma()) +
theme_dark()
ggplot(data = NVDA, aes(x=NVDA.Date)) +
geom_line(aes(y = NVDA.EMA_cl_1W, color = '1-Week')) +
geom_line(aes(y = NVDA.EMA_cl_2W, color = '2-Week')) +
geom_line(aes(y = NVDA.EMA_cl_1M, color = '1-Month')) +
geom_line(aes(y = NVDA.EMA_cl_2M, color = '2-Month')) +
ylab('USD') +
scale_color_manual(values = c(
'1-Week' = 'firebrick1',
'2-Week' = 'chocolate1',
'1-Month' = 'gold',
'2-Month' = 'chartreuse'
)) +
xlab('Date') +
ggtitle("(NVDA) Exponential Moving Average") +
scale_y_continuous( labels = label_comma()) +
theme_dark()
ggplot(data = INTC, aes(x=INTC.Date)) +
geom_line(aes(y = INTC.EMA_cl_1W, color = '1-Week')) +
geom_line(aes(y = INTC.EMA_cl_2W, color = '2-Week')) +
geom_line(aes(y = INTC.EMA_cl_1M, color = '1-Month')) +
geom_line(aes(y = INTC.EMA_cl_2M, color = '2-Month')) +
ylab('USD') +
scale_color_manual(values = c(
'1-Week' = 'firebrick1',
'2-Week' = 'chocolate1',
'1-Month' = 'gold',
'2-Month' = 'chartreuse'
)) +
xlab('Date') +
ggtitle("(INTC) Exponential Moving Average") +
scale_y_continuous( labels = label_comma()) +
theme_dark()
ggplot(data = TSM, aes(x=TSM.Date)) +
geom_line(aes(y = TSM.EMA_cl_1W, color = '1-Week')) +
geom_line(aes(y = TSM.EMA_cl_2W, color = '2-Week')) +
geom_line(aes(y = TSM.EMA_cl_1M, color = '1-Month')) +
geom_line(aes(y = TSM.EMA_cl_2M, color = '2-Month')) +
ylab('USD') +
scale_color_manual(values = c(
'1-Week' = 'firebrick1',
'2-Week' = 'chocolate1',
'1-Month' = 'gold',
'2-Month' = 'chartreuse'
)) +
xlab('Date') +
ggtitle("(TSM) Exponential Moving Average") +
scale_y_continuous( labels = label_comma()) +
theme_dark()
While the plots of the simple moving average and exponential average look very similar to one another, one notable difference is that the exponential average does not “smooth out” the curve as much — this is simply due to the fact that any recent volatility affects the exponential moving average much more than the simple moving average, since volatility in recent events is weighed more heavily.
Simple Moving Deviation of Closing Price
With a concrete notion of the simple moving average as the mean taken
over our lag variables, a natural extension is to also measure the
standard deviation of our lag variables as well to gain an accurate
insight on the volatility of our time series. In fact, the simple moving
deviation has a very particular name in terms of stock prices:
Bollinger Bands. In the very first graphs plotted at
the beginning of this analysis (in the Loading Packages and
Data chapter) using the chartSeries command, the
gray-dotted lines running through the stock values is simply the 20-day
SMA, and the red-dotted lines above and below the stock values are the
20-day simple moving deviation (which are referred to in the chart as
the Bollinger bands). For the sake of completeness, the simple moving
deviation can be calculated as \[
\operatorname{SMD}(X_i, n) = \sqrt{ \frac{\sum_{j=0}^{n-1} (X_{i-j} -
\operatorname{SMA}(X_i, n))^2}{n-1} }
\] As with the simple moving average, we could alternatively
consider the variation where the current data point is not accounted for
in the simple moving deviation by instead ranging \(1 \leq j \leq n\).
simple_moving_deviation <- function(my_vec, lag_period) {
#' Takes the running standard deviation of a column vector
#'
#' Creates a new column vector whose entries are the standard deviation of the previous lag_period entries.
#' When not enough data is available to take the deviation over lag_period, the closest possible
#' average will be taken (for example, if lag_period = 10, then the first 2nd entry of the output
#' vector will simply be the average of the first two values, the 3rd entry of the output vector
#' will be the average of the first three values, and so forth.)
#'
#' @param my_vec the column vector to take the standard deviation of
#' @param lag_period the number of days one wishes to average over
#'
#' @return A vector whose entries represent the standard deviation of the previous lag_period entries in my_vec
# Error handling
if(is.vector(my_vec) == FALSE){
stop("Not Vector: First argument of simple_moving_average must be a vector")
}
if(is.numeric(my_vec[1]) == FALSE){
stop("Non-numeric Entries: values of vector in first argument must be numeric.")
}
if(is.numeric(lag_period) == FALSE || lag_period != round(lag_period)){
stop("Not Integer: Second argument of simple_moving_average must be an integer larger than or equal to 2")
}
if(lag_period <= 1){
stop("Not Large Enough: Second argument of simple_moving_average must be an integer larger than or equal to 2")
}
# return variable
output_vec = c()
# Setting the first standard deviation to 0 and beginning the loop
# at 2 prevents a divide by 0 error without adding an additional if-else branch
# in the loop
output_vec[1] = 0
for (i in 2:length(my_vec)) {
# If there are less that lag_period of data previous to the current date,
# simply take the average of all the days prior to get the closest thing
# to a running average
if (i <= lag_period){
output_vec[i] = sd(my_vec[1:i])
}
else {
output_vec[i] = sd(my_vec[(i-lag_period+1):i])
}
}
return(output_vec)
}
# Compute the simple moving deviation of AMD
AMD$AMD.SMD_cl_1W <- simple_moving_deviation(AMD$AMD.Close, 5)
AMD$AMD.SMD_cl_2W <- simple_moving_deviation(AMD$AMD.Close, 10)
AMD$AMD.SMD_cl_1M <- simple_moving_deviation(AMD$AMD.Close, 20)
AMD$AMD.SMD_cl_2M <- simple_moving_deviation(AMD$AMD.Close, 40)
# Compute the simple moving deviation of NVDA
NVDA$NVDA.SMD_cl_1W <- simple_moving_deviation(NVDA$NVDA.Close, 5)
NVDA$NVDA.SMD_cl_2W <- simple_moving_deviation(NVDA$NVDA.Close, 10)
NVDA$NVDA.SMD_cl_1M <- simple_moving_deviation(NVDA$NVDA.Close, 20)
NVDA$NVDA.SMD_cl_2M <- simple_moving_deviation(NVDA$NVDA.Close, 40)
# Compute the simple moving deviation of INTC
INTC$INTC.SMD_cl_1W <- simple_moving_deviation(INTC$INTC.Close, 5)
INTC$INTC.SMD_cl_2W <- simple_moving_deviation(INTC$INTC.Close, 10)
INTC$INTC.SMD_cl_1M <- simple_moving_deviation(INTC$INTC.Close, 20)
INTC$INTC.SMD_cl_2M <- simple_moving_deviation(INTC$INTC.Close, 40)
# Compute the simple moving deviation of TSM
TSM$TSM.SMD_cl_1W <- simple_moving_deviation(TSM$TSM.Close, 5)
TSM$TSM.SMD_cl_2W <- simple_moving_deviation(TSM$TSM.Close, 10)
TSM$TSM.SMD_cl_1M <- simple_moving_deviation(TSM$TSM.Close, 20)
TSM$TSM.SMD_cl_2M <- simple_moving_deviation(TSM$TSM.Close, 40)
# Plot the simple moving deviation for our four stocks
ggplot(data = AMD, aes(x=AMD.Date)) +
geom_line(aes(y = AMD.SMD_cl_1W, color = '1-Week')) +
geom_line(aes(y = AMD.SMD_cl_2W, color = '2-Week')) +
geom_line(aes(y = AMD.SMD_cl_1M, color = '1-Month')) +
geom_line(aes(y = AMD.SMD_cl_2M, color = '2-Month')) +
ylab('USD') +
scale_color_manual(values = c(
'1-Week' = 'firebrick1',
'2-Week' = 'chocolate1',
'1-Month' = 'gold',
'2-Month' = 'chartreuse'
)) +
xlab('Date') +
ggtitle("(AMD) Simple Moving Deviation") +
scale_y_continuous( labels = label_comma()) +
theme_dark()
ggplot(data = NVDA, aes(x=NVDA.Date)) +
geom_line(aes(y = NVDA.SMD_cl_1W, color = '1-Week')) +
geom_line(aes(y = NVDA.SMD_cl_2W, color = '2-Week')) +
geom_line(aes(y = NVDA.SMD_cl_1M, color = '1-Month')) +
geom_line(aes(y = NVDA.SMD_cl_2M, color = '2-Month')) +
ylab('USD') +
scale_color_manual(values = c(
'1-Week' = 'firebrick1',
'2-Week' = 'chocolate1',
'1-Month' = 'gold',
'2-Month' = 'chartreuse'
)) +
xlab('Date') +
ggtitle("(NVDA) Simple Moving Deviation") +
scale_y_continuous( labels = label_comma()) +
theme_dark()
ggplot(data = INTC, aes(x=INTC.Date)) +
geom_line(aes(y = INTC.SMD_cl_1W, color = '1-Week')) +
geom_line(aes(y = INTC.SMD_cl_2W, color = '2-Week')) +
geom_line(aes(y = INTC.SMD_cl_1M, color = '1-Month')) +
geom_line(aes(y = INTC.SMD_cl_2M, color = '2-Month')) +
ylab('USD') +
scale_color_manual(values = c(
'1-Week' = 'firebrick1',
'2-Week' = 'chocolate1',
'1-Month' = 'gold',
'2-Month' = 'chartreuse'
)) +
xlab('Date') +
ggtitle("(INTC) Simple Moving Deviation") +
scale_y_continuous( labels = label_comma()) +
theme_dark()
ggplot(data = TSM, aes(x=TSM.Date)) +
geom_line(aes(y = TSM.SMD_cl_1W, color = '1-Week')) +
geom_line(aes(y = TSM.SMD_cl_2W, color = '2-Week')) +
geom_line(aes(y = TSM.SMD_cl_1M, color = '1-Month')) +
geom_line(aes(y = TSM.SMD_cl_2M, color = '2-Month')) +
ylab('USD') +
scale_color_manual(values = c(
'1-Week' = 'firebrick1',
'2-Week' = 'chocolate1',
'1-Month' = 'gold',
'2-Month' = 'chartreuse'
)) +
xlab('Date') +
ggtitle("(TSM) Simple Moving Deviation") +
scale_y_continuous( labels = label_comma()) +
theme_dark()
Ultimately, plotting our simple moving deviation without the relevant simple moving averages is not terribly insightful; as one would expect, there is more variation across longer periods than there is across shorter periods.
Moving Average Convergence Divergence (MACD)
The last metric we wish to consider in this analysis is closely related to the crossing of SMA curves in the subsection above; the Moving Average Convergence Divergence (MACD) is simply a value which indicates the curve crossing of the exponential moving average, as that carries greater information about the recent behavior of the data. In most stock market analysis, it is standard to consider the short-term EMA to be taken over a 2-week period and the long-term EMA to be taken over a 1-month period; thus, we define \[ \operatorname{MACD}(X_i) = \operatorname{EMA}(X_i,\ 10) - \operatorname{EMA}(X_i,\ 20) \] In the general study of time-series, the MACD is just a particular example of a curve-crossing metric between moving averages used to predict trend changes — any two long-term and short-term periods could be used to define a similar metric. In the graphs below, a curve crossing the horizontal axis acts as a trade signal to investors to either purchase or short the security depending on whether the curve is crossing into the upper half-plane or lower half-plane.
# Compute the MACD for our 4 stocks
AMD$AMD.MACD = (AMD$AMD.EMA_cl_2W - AMD$AMD.EMA_cl_1M)
NVDA$NVDA.MACD = (NVDA$NVDA.EMA_cl_2W - NVDA$NVDA.EMA_cl_1M)
INTC$INTC.MACD = (INTC$INTC.EMA_cl_2W - INTC$INTC.EMA_cl_1M)
TSM$TSM.MACD = (TSM$TSM.EMA_cl_2W - TSM$TSM.EMA_cl_1M)
# Plot the MACD line
ggplot(data = AMD, aes(x=AMD.Date)) +
geom_line(aes(y = AMD.MACD, color = 'MACD')) +
ylab('USD') +
scale_color_manual(values = c(
'MACD' = 'aquamarine'
)) +
xlab('Date') +
ggtitle("AMD MACD Line") +
scale_y_continuous( labels = label_comma()) +
theme_dark()
ggplot(data = NVDA, aes(x=NVDA.Date)) +
geom_line(aes(y = NVDA.MACD, color = 'MACD')) +
ylab('USD') +
scale_color_manual(values = c(
'MACD' = 'aquamarine'
)) +
xlab('Date') +
ggtitle("NVDA MACD Line") +
scale_y_continuous( labels = label_comma()) +
theme_dark()
ggplot(data = INTC, aes(x=INTC.Date)) +
geom_line(aes(y = INTC.MACD, color = 'MACD')) +
ylab('USD') +
scale_color_manual(values = c(
'MACD' = 'aquamarine'
)) +
xlab('Date') +
ggtitle("INTC MACD Line") +
scale_y_continuous( labels = label_comma()) +
theme_dark()
ggplot(data = TSM, aes(x=TSM.Date)) +
geom_line(aes(y = TSM.MACD, color = 'MACD')) +
ylab('USD') +
scale_color_manual(values = c(
'MACD' = 'aquamarine'
)) +
xlab('Date') +
ggtitle("TSM MACD Line") +
scale_y_continuous( labels = label_comma()) +
theme_dark()
Data Correlation
While having a large array of predictors is in some sense useful for seeing the whole picture of the semiconductor market for the 2023-2024 fiscal year, there is also a potentially significant amount of unnecessary information. As mentioned prior, the behavior of many of our initial predictors coming from the CSV files are very closely related to one another — the closing price one day is directly tied to the opening price of the following day, and if a stock’s minimum / Low value is increasing that generally means all 4 other predictors (aside from volume) are increasing as well. In addition, comparing the performance between two stocks is generally going to be heavily correlated due to the fact that they both follow the underlying market’s climate.
Ultimately, in order to achieve a good understanding of the correlations between all of our predictors we will need to cross examine several subsets of our predictors to see which predictors are correlated for a single stock, and which predictors are useful for measuring competition between stocks. Dividing our correlation plots into two types, we first examine how the predictors are correlated for a fixed stock, and test this underlying trend accross a subset of our stocks (ASML, INTC, NVDA, and NXPI ):
select(AMD, is.numeric) %>%
cor() %>%
corrplot(method = "circle", type = "lower", diag = FALSE, tl.cex=0.6, title="Correlation Plot")
select(NVDA, NVDA.Close, NVDA.Volume, NVDA.SMD_cl_1W, NVDA.SMD_cl_2W, NVDA.SMD_cl_1M, NVDA.SMD_cl_2M, NVDA.MACD) %>%
cor() %>%
corrplot(method = "circle", type = "lower", diag = FALSE, tl.cex=0.6, title="NVDA Correlation Plot" )
select(INTC, INTC.Close, INTC.Volume, INTC.SMD_cl_1W, INTC.SMD_cl_2W, INTC.SMD_cl_1M, INTC.SMD_cl_2M, INTC.MACD) %>%
cor() %>%
corrplot(method = "circle", type = "lower", diag = FALSE, tl.cex=0.6, title="INTC Correlation Plot")
select(TSM, TSM.Close, TSM.Volume, TSM.SMD_cl_1W, TSM.SMD_cl_2W, TSM.SMD_cl_1M, TSM.SMD_cl_2M, TSM.MACD) %>%
cor() %>%
corrplot(method = "circle", type = "lower", diag = FALSE, tl.cex=0.6, title="TSM Correlation Plot")
Setting Up Models
With a better picture in mind of how our stock prices can be measured from both the given metrics, we can now set up our data and begin training our models. This will be done in several steps, first preparing the data to ensure that our models do not become over-fitted to a particular data-set.
Data Split
One of the primary ways we ensure robustness of our models is by partitioning our data into training and testing data. Foremost, this ensures that our model does not become overfit to the details and noise of our underlying data-set by introducing a portion of the data which is unseen during the training phase (i.e. the testing data). Ultimately, one would want outcome variable to have similar statistics / variance across both the training and testing sets — this is accomplished by stratifying our split about the desired outcome variable.
AMD_split <- initial_split(AMD, prop = 0.7,
strata = AMD.Close)
AMD_train <- training(AMD_split)
AMD_test <- testing(AMD_split)NVDA_split <- initial_split(NVDA, prop = 0.7,
strata = NVDA.Close)
NVDA_train <- training(NVDA_split)
NVDA_test <- testing(NVDA_split)INTC_split <- initial_split(INTC, prop = 0.7,
strata = INTC.Close)
INTC_train <- training(INTC_split)
INTC_test <- testing(INTC_split)TSM_split <- initial_split(TSM, prop = 0.7,
strata = TSM.Close)
TSM_train <- training(TSM_split)
TSM_test <- testing(TSM_split)Model Fitting
AMD_recipe = recipe(AMD.Close ~ AMD.Close_L1 + AMD.Close_L2 + AMD.Close_L3 + AMD.Close_L4 +
AMD.Close_L5 + AMD.Close_L6 + AMD.Close_L7 + AMD.Close_L8 + AMD.Close_L9 +
AMD.Close_L10 + AMD.SMD_cl_1W + AMD.SMA_cl_1W + AMD.MACD,
data=AMD_train) %>%
step_interact(terms= ~ AMD.Close_L1:AMD.Close_L2) %>%
step_interact(terms= ~ AMD.Close_L2:AMD.Close_L3) %>%
step_interact(terms= ~ AMD.Close_L3:AMD.Close_L4) %>%
step_interact(terms= ~ AMD.Close_L4:AMD.Close_L5) %>%
step_interact(terms= ~ AMD.Close_L5:AMD.Close_L6) %>%
step_interact(terms= ~ AMD.Close_L6:AMD.Close_L7) %>%
step_interact(terms= ~ AMD.Close_L7:AMD.Close_L8) %>%
step_interact(terms= ~ AMD.Close_L8:AMD.Close_L9) %>%
step_interact(terms= ~ AMD.Close_L9:AMD.Close_L10) %>%
step_center(all_predictors()) %>%
step_scale(all_predictors())NVDA_recipe = recipe(NVDA.Close ~ NVDA.Close_L1 + NVDA.Close_L2 + NVDA.Close_L3 + NVDA.Close_L4 + NVDA.Close_L5 +
NVDA.Close_L6 + NVDA.Close_L7 + NVDA.Close_L8 + NVDA.Close_L9 + NVDA.Close_L10 +
NVDA.SMD_cl_1W + NVDA.SMA_cl_1W + NVDA.MACD,
data=NVDA_train) %>%
step_interact(terms= ~ NVDA.Close_L1:NVDA.Close_L2) %>%
step_interact(terms= ~ NVDA.Close_L2:NVDA.Close_L3) %>%
step_interact(terms= ~ NVDA.Close_L3:NVDA.Close_L4) %>%
step_interact(terms= ~ NVDA.Close_L4:NVDA.Close_L5) %>%
step_interact(terms= ~ NVDA.Close_L5:NVDA.Close_L6) %>%
step_interact(terms= ~ NVDA.Close_L6:NVDA.Close_L7) %>%
step_interact(terms= ~ NVDA.Close_L7:NVDA.Close_L8) %>%
step_interact(terms= ~ NVDA.Close_L8:NVDA.Close_L9) %>%
step_interact(terms= ~ NVDA.Close_L9:NVDA.Close_L10) %>%
step_center(all_predictors()) %>%
step_scale(all_predictors())INTC_recipe = recipe(INTC.Close ~ INTC.Close_L1 + INTC.Close_L2 + INTC.Close_L3 + INTC.Close_L4 +
INTC.Close_L5 + INTC.Close_L6 + INTC.Close_L7 + INTC.Close_L8 + INTC.Close_L9 + INTC.Close_L10 +
INTC.SMD_cl_1W + INTC.SMA_cl_1W + INTC.EMA_cl_1W + INTC.MACD,
data=INTC_train) %>%
step_interact(terms= ~ INTC.Close_L1:INTC.Close_L2) %>%
step_interact(terms= ~ INTC.Close_L2:INTC.Close_L3) %>%
step_interact(terms= ~ INTC.Close_L3:INTC.Close_L4) %>%
step_interact(terms= ~ INTC.Close_L4:INTC.Close_L5) %>%
step_interact(terms= ~ INTC.Close_L5:INTC.Close_L6) %>%
step_interact(terms= ~ INTC.Close_L6:INTC.Close_L7) %>%
step_interact(terms= ~ INTC.Close_L7:INTC.Close_L8) %>%
step_interact(terms= ~ INTC.Close_L8:INTC.Close_L9) %>%
step_interact(terms= ~ INTC.Close_L9:INTC.Close_L10) %>%
step_center(all_predictors()) %>%
step_scale(all_predictors())TSM_recipe = recipe(TSM.Close ~ TSM.Close_L1 + TSM.Close_L2 + TSM.Close_L3 + TSM.Close_L4 +
TSM.Close_L5 + TSM.Close_L6 + TSM.Close_L7 + TSM.Close_L8 + TSM.Close_L9 + TSM.Close_L10 +
TSM.SMD_cl_1W + TSM.SMA_cl_1W + TSM.EMA_cl_1W + TSM.MACD,
data=TSM_train) %>%
step_interact(terms= ~ TSM.Close_L1:TSM.Close_L2) %>%
step_interact(terms= ~ TSM.Close_L2:TSM.Close_L3) %>%
step_interact(terms= ~ TSM.Close_L3:TSM.Close_L4) %>%
step_interact(terms= ~ TSM.Close_L4:TSM.Close_L5) %>%
step_interact(terms= ~ TSM.Close_L5:TSM.Close_L6) %>%
step_interact(terms= ~ TSM.Close_L6:TSM.Close_L7) %>%
step_interact(terms= ~ TSM.Close_L7:TSM.Close_L8) %>%
step_interact(terms= ~ TSM.Close_L8:TSM.Close_L9) %>%
step_interact(terms= ~ TSM.Close_L9:TSM.Close_L10) %>%
step_center(all_predictors()) %>%
step_scale(all_predictors())k-Fold Cross Validation
AMD_folds <- vfold_cv(AMD_train, v = 10, strata = AMD.Close)
NVDA_folds <- vfold_cv(NVDA_train, v = 10, strata = NVDA.Close)
INTC_folds <- vfold_cv(INTC_train, v = 10, strata = INTC.Close)
TSM_folds <- vfold_cv(TSM_train, v = 10, strata = TSM.Close)Fitting the Models
# Linear Regression
lm_model <- linear_reg() %>%
set_engine("lm")
# Ridge Regression
ridge_model <- linear_reg(mixture = 0,
penalty = tune()) %>%
set_mode("regression") %>%
set_engine("glmnet")
# Lasso Regression
lasso_model <- linear_reg(mixture = 1,
penalty = tune()) %>%
set_mode("regression") %>%
set_engine("glmnet")
# Elastic Net
elastic_net_model <- linear_reg(mixture = tune(),
penalty = tune()) %>%
set_mode("regression") %>%
set_engine("glmnet")
# k-Nearest Neighbors
knn_model <- nearest_neighbor(neighbors = tune()) %>%
set_engine("kknn") %>%
set_mode("regression")Set Up Workflows
# Linear Regression Workflows
lm_wflow_AMD <- workflow() %>%
add_model(lm_model) %>%
add_recipe(AMD_recipe)
# Ridge Regression Workflows
ridge_wflow_AMD <- workflow() %>%
add_model(ridge_model) %>%
add_recipe(AMD_recipe)
# Lasso Regression Workflows
lasso_wflow_AMD <- workflow() %>%
add_model(lasso_model) %>%
add_recipe(AMD_recipe)
# Elastic Net Workflows
elastic_net_wflow_AMD <- workflow() %>%
add_model(elastic_net_model) %>%
add_recipe(AMD_recipe)
# k-Nearest Neighbors Workflows
knn_wflow_AMD <- workflow() %>%
add_model(knn_model) %>%
add_recipe(AMD_recipe)# Linear Regression Workflows
lm_wflow_NVDA <- workflow() %>%
add_model(lm_model) %>%
add_recipe(NVDA_recipe)
# Ridge Regression Workflows
ridge_wflow_NVDA <- workflow() %>%
add_model(ridge_model) %>%
add_recipe(NVDA_recipe)
# Lasso Regression Workflows
lasso_wflow_NVDA <- workflow() %>%
add_model(lasso_model) %>%
add_recipe(NVDA_recipe)
# Elastic Net Workflows
elastic_net_wflow_NVDA <- workflow() %>%
add_model(elastic_net_model) %>%
add_recipe(NVDA_recipe)
# k-Nearest Neighbors Workflows
knn_wflow_NVDA <- workflow() %>%
add_model(knn_model) %>%
add_recipe(NVDA_recipe)# Linear Regression Workflows
lm_wflow_INTC <- workflow() %>%
add_model(lm_model) %>%
add_recipe(INTC_recipe)
# Ridge Regression Workflows
ridge_wflow_INTC <- workflow() %>%
add_model(ridge_model) %>%
add_recipe(INTC_recipe)
# Lasso Regression Workflows
lasso_wflow_INTC <- workflow() %>%
add_model(lasso_model) %>%
add_recipe(INTC_recipe)
# Elastic Net Workflows
elastic_net_wflow_INTC <- workflow() %>%
add_model(elastic_net_model) %>%
add_recipe(INTC_recipe)
# k-Nearest Neighbors Workflows
knn_wflow_INTC <- workflow() %>%
add_model(knn_model) %>%
add_recipe(INTC_recipe)# Linear Regression Workflows
lm_wflow_TSM <- workflow() %>%
add_model(lm_model) %>%
add_recipe(TSM_recipe)
# Ridge Regression Workflows
ridge_wflow_TSM <- workflow() %>%
add_model(ridge_model) %>%
add_recipe(TSM_recipe)
# Lasso Regression Workflows
lasso_wflow_TSM <- workflow() %>%
add_model(lasso_model) %>%
add_recipe(TSM_recipe)
# Elastic Net Workflows
elastic_net_wflow_TSM <- workflow() %>%
add_model(elastic_net_model) %>%
add_recipe(TSM_recipe)
# k-Nearest Neighbors Workflows
knn_wflow_TSM <- workflow() %>%
add_model(knn_model) %>%
add_recipe(TSM_recipe)Hyperparameter Tuning
Set up Grids:
# Grid for Ridge Regression and Lasso Regression
no_mixture_grid <- grid_regular(penalty(range = c(0,1)), levels = 50)
# Grid for Elastic Net
elastic_net_grid <- grid_regular(penalty(range = c(0, 1),
trans = identity_trans()),
mixture(range = c(0, 1)),
levels = 10)
# k-Nearest Neighbors Net
knn_grid <- grid_regular(neighbors(range = c(2,20)), levels = 10)# Find optimal parameters for ridge regression
ridge_tune_AMD <- tune_grid(
ridge_wflow_AMD,
resamples = AMD_folds,
grid = no_mixture_grid
)
ridge_final_wflow_AMD <- select_best(ridge_tune_AMD , metric="rmse" ) %>%
finalize_workflow(x=ridge_wflow_AMD )
# Find optimal parameters for lasso regression
lasso_tune_AMD <- tune_grid(
lasso_wflow_AMD ,
resamples = AMD_folds,
grid = no_mixture_grid
)
lasso_final_wflow_AMD <- select_best(lasso_tune_AMD , metric="rmse") %>%
finalize_workflow(x=lasso_wflow_AMD )
# Find optimal parameters for Elastic Net
elastic_net_tune_AMD <- tune_grid(
elastic_net_wflow_AMD ,
resamples = AMD_folds,
grid = elastic_net_grid
)
elastic_net_final_wflow_AMD <- select_best(elastic_net_tune_AMD , metric = "rmse") %>%
finalize_workflow(x=elastic_net_wflow_AMD )
# Find optimal parameters for k-Nearest Neighbors
knn_tune_AMD <- tune_grid(
knn_wflow_AMD ,
resamples = AMD_folds,
grid = knn_grid
)
knn_final_wflow_AMD <- select_best(knn_tune_AMD , metric = "rmse") %>%
finalize_workflow(x=knn_wflow_AMD )# Find optimal parameters for ridge regression
ridge_tune_NVDA <- tune_grid(
ridge_wflow_NVDA,
resamples = NVDA_folds,
grid = no_mixture_grid
)
ridge_final_wflow_NVDA <- select_best(ridge_tune_NVDA , metric="rmse" ) %>%
finalize_workflow(x=ridge_wflow_NVDA )
# Find optimal parameters for lasso regression
lasso_tune_NVDA <- tune_grid(
lasso_wflow_NVDA ,
resamples = NVDA_folds,
grid = no_mixture_grid
)
lasso_final_wflow_NVDA <- select_best(lasso_tune_NVDA , metric="rmse") %>%
finalize_workflow(x=lasso_wflow_NVDA )
# Find optimal parameters for Elastic Net
elastic_net_tune_NVDA <- tune_grid(
elastic_net_wflow_NVDA ,
resamples = NVDA_folds,
grid = elastic_net_grid
)
elastic_net_final_wflow_NVDA <- select_best(elastic_net_tune_NVDA , metric = "rmse") %>%
finalize_workflow(x=elastic_net_wflow_NVDA )
# Find optimal parameters for k-Nearest Neighbors
knn_tune_NVDA <- tune_grid(
knn_wflow_NVDA ,
resamples = NVDA_folds,
grid = knn_grid
)
knn_final_wflow_NVDA <- select_best(knn_tune_NVDA , metric = "rmse") %>%
finalize_workflow(x=knn_wflow_NVDA )# Find optimal parameters for ridge regression
ridge_tune_INTC <- tune_grid(
ridge_wflow_INTC,
resamples = INTC_folds,
grid = no_mixture_grid
)
ridge_final_wflow_INTC <- select_best(ridge_tune_INTC , metric="rmse" ) %>%
finalize_workflow(x=ridge_wflow_INTC )
# Find optimal parameters for lasso regression
lasso_tune_INTC <- tune_grid(
lasso_wflow_INTC ,
resamples = INTC_folds,
grid = no_mixture_grid
)## → A | warning: A correlation computation is required, but `estimate` is constant and has 0
## standard deviation, resulting in a divide by 0 error. `NA` will be returned.## There were issues with some computations A: x1There were issues with some computations A: x2There were issues with some computations A: x3There were issues with some computations A: x4There were issues with some computations A: x5There were issues with some computations A: x6There were issues with some computations A: x7There were issues with some computations A: x8There were issues with some computations A: x9There were issues with some computations A: x10There were issues with some computations A: x10lasso_final_wflow_INTC <- select_best(lasso_tune_INTC , metric="rmse") %>%
finalize_workflow(x=lasso_wflow_INTC )
# Find optimal parameters for Elastic Net
elastic_net_tune_INTC <- tune_grid(
elastic_net_wflow_INTC ,
resamples = INTC_folds,
grid = elastic_net_grid
)
elastic_net_final_wflow_INTC <- select_best(elastic_net_tune_INTC , metric = "rmse") %>%
finalize_workflow(x=elastic_net_wflow_INTC )
# Find optimal parameters for k-Nearest Neighbors
knn_tune_INTC <- tune_grid(
knn_wflow_INTC ,
resamples = INTC_folds,
grid = knn_grid
)
knn_final_wflow_INTC <- select_best(knn_tune_INTC , metric = "rmse") %>%
finalize_workflow(x=knn_wflow_INTC )# Find optimal parameters for ridge regression
ridge_tune_TSM <- tune_grid(
ridge_wflow_TSM,
resamples = TSM_folds,
grid = no_mixture_grid
)
ridge_final_wflow_TSM <- select_best(ridge_tune_TSM , metric="rmse" ) %>%
finalize_workflow(x=ridge_wflow_TSM )
# Find optimal parameters for lasso regression
lasso_tune_TSM <- tune_grid(
lasso_wflow_TSM ,
resamples = TSM_folds,
grid = no_mixture_grid
)## → A | warning: A correlation computation is required, but `estimate` is constant and has 0
## standard deviation, resulting in a divide by 0 error. `NA` will be returned.## There were issues with some computations A: x1There were issues with some computations A: x2There were issues with some computations A: x3There were issues with some computations A: x4There were issues with some computations A: x5There were issues with some computations A: x6There were issues with some computations A: x7There were issues with some computations A: x8There were issues with some computations A: x9There were issues with some computations A: x10There were issues with some computations A: x10lasso_final_wflow_TSM <- select_best(lasso_tune_TSM , metric="rmse") %>%
finalize_workflow(x=lasso_wflow_TSM )
# Find optimal parameters for Elastic Net
elastic_net_tune_TSM <- tune_grid(
elastic_net_wflow_TSM ,
resamples = TSM_folds,
grid = elastic_net_grid
)
elastic_net_final_wflow_TSM <- select_best(elastic_net_tune_TSM , metric = "rmse") %>%
finalize_workflow(x=elastic_net_wflow_TSM )
# Find optimal parameters for k-Nearest Neighbors
knn_tune_TSM <- tune_grid(
knn_wflow_TSM ,
resamples = TSM_folds,
grid = knn_grid
)
knn_final_wflow_TSM <- select_best(knn_tune_TSM , metric = "rmse") %>%
finalize_workflow(x=knn_wflow_TSM )Model Fitting
# Linear Regression Fits
lm_fit_AMD <- fit(lm_wflow_AMD, AMD_train)
# Ridge Regression Fits
ridge_fit_AMD <- fit(ridge_final_wflow_AMD , AMD_train)
# Lasso Regression Fits
lasso_fit_AMD <- fit(lasso_final_wflow_AMD , AMD_train)
# Elastic Net Fits
elastic_net_fit_AMD <- fit(elastic_net_final_wflow_AMD , AMD_train)
# k-Nearest Neighbors Fit
knn_fit_AMD <- fit(knn_final_wflow_AMD , AMD_train)# Linear Regression Fits
lm_fit_NVDA <- fit(lm_wflow_NVDA, NVDA_train)
# Ridge Regression Fits
ridge_fit_NVDA <- fit(ridge_final_wflow_NVDA , NVDA_train)
# Lasso Regression Fits
lasso_fit_NVDA <- fit(lasso_final_wflow_NVDA , NVDA_train)
# Elastic Net Fits
elastic_net_fit_NVDA <- fit(elastic_net_final_wflow_NVDA , NVDA_train)
# k-Nearest Neighbors Fit
knn_fit_NVDA <- fit(knn_final_wflow_NVDA , NVDA_train)# Linear Regression Fits
lm_fit_INTC <- fit(lm_wflow_INTC, INTC_train)
# Ridge Regression Fits
ridge_fit_INTC <- fit(ridge_final_wflow_INTC , INTC_train)
# Lasso Regression Fits
lasso_fit_INTC <- fit(lasso_final_wflow_INTC , INTC_train)
# Elastic Net Fits
elastic_net_fit_INTC <- fit(elastic_net_final_wflow_INTC , INTC_train)
# k-Nearest Neighbors Fit
knn_fit_INTC <- fit(knn_final_wflow_INTC , INTC_train)# Linear Regression Fits
lm_fit_TSM <- fit(lm_wflow_TSM, TSM_train)
# Ridge Regression Fits
ridge_fit_TSM <- fit(ridge_final_wflow_TSM , TSM_train)
# Lasso Regression Fits
lasso_fit_TSM <- fit(lasso_final_wflow_TSM , TSM_train)
# Elastic Net Fits
elastic_net_fit_TSM <- fit(elastic_net_final_wflow_TSM , TSM_train)
# k-Nearest Neighbors Fit
knn_fit_TSM <- fit(knn_final_wflow_TSM , TSM_train)Model Results
# Linear Regression Training
lm_train_res_AMD <- predict(lm_fit_AMD , new_data = AMD_train %>% select(-AMD.Close))
lm_train_res_AMD <- bind_cols(lm_train_res_AMD , AMD_train %>% select(AMD.Close))
# Ridge Regression Training
ridge_train_res_AMD <- predict(ridge_fit_AMD , new_data = AMD_train %>% select(-AMD.Close))
ridge_train_res_AMD <- bind_cols(ridge_train_res_AMD , AMD_train %>% select(AMD.Close))
# Lasso Regression Training
lasso_train_res_AMD <- predict(lasso_fit_AMD , new_data = AMD_train %>% select(-AMD.Close))
lasso_train_res_AMD <- bind_cols(lasso_train_res_AMD , AMD_train %>% select(AMD.Close))
# Elastic Net Training
elastic_net_train_res_AMD <- predict(elastic_net_fit_AMD , new_data = AMD_train %>% select(-AMD.Close ))
elastic_net_train_res_AMD <- bind_cols(elastic_net_train_res_AMD , AMD_train %>% select(AMD.Close ))
# k-Nearest Neighbors Training
knn_train_res_AMD <- predict(knn_fit_AMD , new_data = AMD_train %>% select(-AMD.Close ))
knn_train_res_AMD <- bind_cols(knn_train_res_AMD , AMD_train %>% select(AMD.Close ))# Linear Regression Training
lm_train_res_NVDA <- predict(lm_fit_NVDA , new_data = NVDA_train %>% select(-NVDA.Close))
lm_train_res_NVDA <- bind_cols(lm_train_res_NVDA , NVDA_train %>% select(NVDA.Close))
# Ridge Regression Training
ridge_train_res_NVDA <- predict(ridge_fit_NVDA , new_data = NVDA_train %>% select(-NVDA.Close))
ridge_train_res_NVDA <- bind_cols(ridge_train_res_NVDA , NVDA_train %>% select(NVDA.Close))
# Lasso Regression Training
lasso_train_res_NVDA <- predict(lasso_fit_NVDA , new_data = NVDA_train %>% select(-NVDA.Close))
lasso_train_res_NVDA <- bind_cols(lasso_train_res_NVDA , NVDA_train %>% select(NVDA.Close))
# Elastic Net Training
elastic_net_train_res_NVDA <- predict(elastic_net_fit_NVDA , new_data = NVDA_train %>% select(-NVDA.Close ))
elastic_net_train_res_NVDA <- bind_cols(elastic_net_train_res_NVDA , NVDA_train %>% select(NVDA.Close ))
# k-Nearest Neighbors Training
knn_train_res_NVDA <- predict(knn_fit_NVDA , new_data = NVDA_train %>% select(-NVDA.Close ))
knn_train_res_NVDA <- bind_cols(knn_train_res_NVDA , NVDA_train %>% select(NVDA.Close ))# Linear Regression Training
lm_train_res_INTC <- predict(lm_fit_INTC , new_data = INTC_train %>% select(-INTC.Close))
lm_train_res_INTC <- bind_cols(lm_train_res_INTC , INTC_train %>% select(INTC.Close))
# Ridge Regression Training
ridge_train_res_INTC <- predict(ridge_fit_INTC , new_data = INTC_train %>% select(-INTC.Close))
ridge_train_res_INTC <- bind_cols(ridge_train_res_INTC , INTC_train %>% select(INTC.Close))
# Lasso Regression Training
lasso_train_res_INTC <- predict(lasso_fit_INTC , new_data = INTC_train %>% select(-INTC.Close))
lasso_train_res_INTC <- bind_cols(lasso_train_res_INTC , INTC_train %>% select(INTC.Close))
# Elastic Net Training
elastic_net_train_res_INTC <- predict(elastic_net_fit_INTC , new_data = INTC_train %>% select(-INTC.Close ))
elastic_net_train_res_INTC <- bind_cols(elastic_net_train_res_INTC , INTC_train %>% select(INTC.Close ))
# k-Nearest Neighbors Training
knn_train_res_INTC <- predict(knn_fit_INTC , new_data = INTC_train %>% select(-INTC.Close ))
knn_train_res_INTC <- bind_cols(knn_train_res_INTC , INTC_train %>% select(INTC.Close ))# Linear Regression Training
lm_train_res_TSM <- predict(lm_fit_TSM , new_data = TSM_train %>% select(-TSM.Close))
lm_train_res_TSM <- bind_cols(lm_train_res_TSM , TSM_train %>% select(TSM.Close))
# Ridge Regression Training
ridge_train_res_TSM <- predict(ridge_fit_TSM , new_data = TSM_train %>% select(-TSM.Close))
ridge_train_res_TSM <- bind_cols(ridge_train_res_TSM , TSM_train %>% select(TSM.Close))
# Lasso Regression Training
lasso_train_res_TSM <- predict(lasso_fit_TSM , new_data = TSM_train %>% select(-TSM.Close))
lasso_train_res_TSM <- bind_cols(lasso_train_res_TSM , TSM_train %>% select(TSM.Close))
# Elastic Net Training
elastic_net_train_res_TSM <- predict(elastic_net_fit_TSM , new_data = TSM_train %>% select(-TSM.Close ))
elastic_net_train_res_TSM <- bind_cols(elastic_net_train_res_TSM , TSM_train %>% select(TSM.Close ))
# k-Nearest Neighbors Training
knn_train_res_TSM <- predict(knn_fit_TSM , new_data = TSM_train %>% select(-TSM.Close ))
knn_train_res_TSM <- bind_cols(knn_train_res_TSM , TSM_train %>% select(TSM.Close ))Model Accuracies
Root Mean Square Error (RMSE) results:
tibble(Model = c("Linear Regression", "Ridge Regression", "Lasso Regression", "Elastic Net", "k-Nearest Neighbors"),
AMD = c((lm_train_res_AMD %>% rmse( AMD.Close, .pred))$.estimate,
(ridge_train_res_AMD %>% rmse( AMD.Close, .pred))$.estimate,
(lasso_train_res_AMD %>% rmse( AMD.Close, .pred))$.estimate,
(elastic_net_train_res_AMD %>% rmse( AMD.Close, .pred))$.estimate,
(knn_train_res_AMD %>% rmse( AMD.Close, .pred))$.estimate ),
NVDA = c((lm_train_res_NVDA %>% rmse( NVDA.Close, .pred))$.estimate,
(ridge_train_res_NVDA %>% rmse( NVDA.Close, .pred))$.estimate,
(lasso_train_res_NVDA %>% rmse( NVDA.Close, .pred))$.estimate,
(elastic_net_train_res_NVDA %>% rmse( NVDA.Close, .pred))$.estimate,
(knn_train_res_NVDA %>% rmse( NVDA.Close, .pred))$.estimate ),
INTC = c((lm_train_res_INTC %>% rmse( INTC.Close, .pred))$.estimate,
(ridge_train_res_INTC %>% rmse( INTC.Close, .pred))$.estimate,
(lasso_train_res_INTC %>% rmse( INTC.Close, .pred))$.estimate,
(elastic_net_train_res_INTC %>% rmse( INTC.Close, .pred))$.estimate,
(knn_train_res_INTC %>% rmse( INTC.Close, .pred))$.estimate ),
TSM = c((lm_train_res_TSM %>% rmse( TSM.Close, .pred))$.estimate,
(ridge_train_res_TSM %>% rmse( TSM.Close, .pred))$.estimate,
(lasso_train_res_TSM %>% rmse( TSM.Close, .pred))$.estimate,
(elastic_net_train_res_TSM %>% rmse( TSM.Close, .pred))$.estimate,
(knn_train_res_TSM %>% rmse( TSM.Close, .pred))$.estimate )
) %>%
kable() %>%
kable_styling(full_width = F) %>%
scroll_box(width = "100%", height = "200px")| Model | AMD | NVDA | INTC | TSM |
|---|---|---|---|---|
| Linear Regression | 0.0529450 | 0.492420 | 0.0000000 | 0.0948985 |
| Ridge Regression | 3.1090870 | 12.717839 | 1.0051845 | 1.5427664 |
| Lasso Regression | 2.9645541 | 9.544530 | 1.2526970 | 1.7299049 |
| Elastic Net | 0.5595055 | 5.337853 | 0.1712020 | 0.2013565 |
| k-Nearest Neighbors | 1.4430606 | 4.906444 | 0.1501175 | 0.5515341 |
R^2 results:
tibble(Model = c("Linear Regression", "Ridge Regression", "Lasso Regression", "Elastic Net", "k-Nearest Neighbors"),
AMD = c((lm_train_res_AMD %>% rsq( AMD.Close, .pred))$.estimate,
(ridge_train_res_AMD %>% rsq( AMD.Close, .pred))$.estimate,
(lasso_train_res_AMD %>% rsq( AMD.Close, .pred))$.estimate,
(elastic_net_train_res_AMD %>% rsq( AMD.Close, .pred))$.estimate,
(knn_train_res_AMD %>% rsq( AMD.Close, .pred))$.estimate ),
NVDA = c((lm_train_res_NVDA %>% rsq( NVDA.Close, .pred))$.estimate,
(ridge_train_res_NVDA %>% rsq( NVDA.Close, .pred))$.estimate,
(lasso_train_res_NVDA %>% rsq( NVDA.Close, .pred))$.estimate,
(elastic_net_train_res_NVDA %>% rsq( NVDA.Close, .pred))$.estimate,
(knn_train_res_NVDA %>% rsq( NVDA.Close, .pred))$.estimate ),
INTC = c((lm_train_res_INTC %>% rsq( INTC.Close, .pred))$.estimate,
(ridge_train_res_INTC %>% rsq( INTC.Close, .pred))$.estimate,
(lasso_train_res_INTC %>% rsq( INTC.Close, .pred))$.estimate,
(elastic_net_train_res_INTC %>% rsq( INTC.Close, .pred))$.estimate,
(knn_train_res_INTC %>% rsq( INTC.Close, .pred))$.estimate ),
TSM = c((lm_train_res_TSM %>% rsq( TSM.Close, .pred))$.estimate,
(ridge_train_res_TSM %>% rsq( TSM.Close, .pred))$.estimate,
(lasso_train_res_TSM %>% rsq( TSM.Close, .pred))$.estimate,
(elastic_net_train_res_TSM %>% rsq( TSM.Close, .pred))$.estimate,
(knn_train_res_TSM %>% rsq( TSM.Close, .pred))$.estimate )
) %>%
kable() %>%
kable_styling(full_width = F) %>%
scroll_box(width = "100%", height = "200px")| Model | AMD | NVDA | INTC | TSM |
|---|---|---|---|---|
| Linear Regression | 0.9999912 | 0.9999792 | 1.0000000 | 0.9997814 |
| Ridge Regression | 0.9696946 | 0.9862282 | 0.9677486 | 0.9431276 |
| Lasso Regression | 0.9755071 | 0.9922683 | 0.9816290 | 0.9517890 |
| Elastic Net | 0.9990249 | 0.9975579 | 0.9990581 | 0.9990305 |
| k-Nearest Neighbors | 0.9936798 | 0.9979592 | 0.9992752 | 0.9930131 |